Solve for $x$ and $y$ using elimination. ${5x+5y = 60}$ ${4x-2y = 30}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $5$ ${-20x-20y = -240}$ $20x-10y = 150$ Add the top and bottom equations together. $-30y = -90$ $\dfrac{-30y}{{-30}} = \dfrac{-90}{{-30}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {5x+5y = 60}\thinspace$ to find $x$ ${5x + 5}{(3)}{= 60}$ $5x+15 = 60$ $5x+15{-15} = 60{-15}$ $5x = 45$ $\dfrac{5x}{{5}} = \dfrac{45}{{5}}$ ${x = 9}$ You can also plug ${y = 3}$ into $\thinspace {4x-2y = 30}\thinspace$ and get the same answer for $x$ : ${4x - 2}{(3)}{= 30}$ ${x = 9}$